568 research outputs found
Structural motifs of biomolecules
Biomolecular structures are assemblies of emergent anisotropic building
modules such as uniaxial helices or biaxial strands. We provide an approach to
understanding a marginally compact phase of matter that is occupied by proteins
and DNA. This phase, which is in some respects analogous to the liquid crystal
phase for chain molecules, stabilizes a range of shapes that can be obtained by
sequence-independent interactions occurring intra- and intermolecularly between
polymeric molecules. We present a singularityfree self-interaction for a tube
in the continuum limit and show that this results in the tube being positioned
in the marginally compact phase. Our work provides a unified framework for
understanding the building blocks of biomolecules.Comment: 13 pages, 5 figure
Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators
We study lasing emission from asymmetric resonant cavity (ARC) GaN
micro-lasers. By comparing far-field intensity patterns with images of the
micro-laser we find that the lasing modes are concentrated on three-bounce
unstable periodic ray orbits, i.e. the modes are scarred. The high-intensity
emission directions of these scarred modes are completely different from those
predicted by applying Snell's law to the ray orbit. This effect is due to the
process of ``Fresnel filtering'' which occurs when a beam of finite angular
spread is incident at the critical angle for total internal reflection.Comment: 4 pages, 3 figures (eps), RevTeX 3.1, submitted to Phys. Rev. Lett;
corrected a minor (transcription) erro
Spin models on random graphs with controlled topologies beyond degree constraints
We study Ising spin models on finitely connected random interaction graphs
which are drawn from an ensemble in which not only the degree distribution
can be chosen arbitrarily, but which allows for further fine-tuning of
the topology via preferential attachment of edges on the basis of an arbitrary
function Q(k,k') of the degrees of the vertices involved. We solve these models
using finite connectivity equilibrium replica theory, within the replica
symmetric ansatz. In our ensemble of graphs, phase diagrams of the spin system
are found to depend no longer only on the chosen degree distribution, but also
on the choice made for Q(k,k'). The increased ability to control interaction
topology in solvable models beyond prescribing only the degree distribution of
the interaction graph enables a more accurate modeling of real-world
interacting particle systems by spin systems on suitably defined random graphs.Comment: 21 pages, 4 figures, submitted to J Phys
Real-Gas Effects and Phase Separation in Underexpanded Jets at Engine-Relevant Conditions
A numerical framework implemented in the open-source tool OpenFOAM is
presented in this work combining a hybrid, pressure-based solver with a
vapor-liquid equilibrium model based on the cubic equation of state. This
framework is used in the present work to investigate underexpanded jets at
engine-relevant conditions where real-gas effects and mixture induced phase
separation are probable to occur. A thorough validation and discussion of the
applied vapor-liquid equilibrium model is conducted by means of general
thermodynamic relations and measurement data available in the literature.
Engine-relevant simulation cases for two different fuels were defined. Analyses
of the flow field show that the used fuel has a first order effect on the
occurrence of phase separation. In the case of phase separation two different
effects could be revealed causing the single-phase instability, namely the
strong expansion and the mixing of the fuel with the chamber gas. A comparison
of single-phase and two-phase jets disclosed that the phase separation leads to
a completely different penetration depth in contrast to single-phase injection
and therefore commonly used analytical approaches fail to predict the
penetration depth.Comment: Preprint submitted to AIAA Scitech 2018, Kissimmee, Florid
Local Anisotropy of Fluids using Minkowski Tensors
Statistics of the free volume available to individual particles have
previously been studied for simple and complex fluids, granular matter,
amorphous solids, and structural glasses. Minkowski tensors provide a set of
shape measures that are based on strong mathematical theorems and easily
computed for polygonal and polyhedral bodies such as free volume cells (Voronoi
cells). They characterize the local structure beyond the two-point correlation
function and are suitable to define indices of
local anisotropy. Here, we analyze the statistics of Minkowski tensors for
configurations of simple liquid models, including the ideal gas (Poisson point
process), the hard disks and hard spheres ensemble, and the Lennard-Jones
fluid. We show that Minkowski tensors provide a robust characterization of
local anisotropy, which ranges from for vapor
phases to for ordered solids. We find that for fluids,
local anisotropy decreases monotonously with increasing free volume and
randomness of particle positions. Furthermore, the local anisotropy indices
are sensitive to structural transitions in these simple
fluids, as has been previously shown in granular systems for the transition
from loose to jammed bead packs
Cell shape analysis of random tessellations based on Minkowski tensors
To which degree are shape indices of individual cells of a tessellation
characteristic for the stochastic process that generates them? Within the
context of stochastic geometry and the physics of disordered materials, this
corresponds to the question of relationships between different stochastic
models. In the context of image analysis of synthetic and biological materials,
this question is central to the problem of inferring information about
formation processes from spatial measurements of resulting random structures.
We address this question by a theory-based simulation study of shape indices
derived from Minkowski tensors for a variety of tessellation models. We focus
on the relationship between two indices: an isoperimetric ratio of the
empirical averages of cell volume and area and the cell elongation quantified
by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for
these quantities, as well as for distributions thereof and for correlations of
cell shape and volume, are presented for Voronoi mosaics of the Poisson point
process, determinantal and permanental point processes, and Gibbs hard-core and
random sequential absorption processes as well as for Laguerre tessellations of
polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data
are complemented by mechanically stable crystalline sphere and disordered
ellipsoid packings and area-minimising foam models. We find that shape indices
of individual cells are not sufficient to unambiguously identify the generating
process even amongst this limited set of processes. However, we identify
significant differences of the shape indices between many of these tessellation
models. Given a realization of a tessellation, these shape indices can narrow
the choice of possible generating processes, providing a powerful tool which
can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their
Applications in Stochastic Geometry and Imaging" in Lecture Notes in
Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense
Minkowski Tensors of Anisotropic Spatial Structure
This article describes the theoretical foundation of and explicit algorithms
for a novel approach to morphology and anisotropy analysis of complex spatial
structure using tensor-valued Minkowski functionals, the so-called Minkowski
tensors. Minkowski tensors are generalisations of the well-known scalar
Minkowski functionals and are explicitly sensitive to anisotropic aspects of
morphology, relevant for example for elastic moduli or permeability of
microstructured materials. Here we derive explicit linear-time algorithms to
compute these tensorial measures for three-dimensional shapes. These apply to
representations of any object that can be represented by a triangulation of its
bounding surface; their application is illustrated for the polyhedral Voronoi
cellular complexes of jammed sphere configurations, and for triangulations of a
biopolymer fibre network obtained by confocal microscopy. The article further
bridges the substantial notational and conceptual gap between the different but
equivalent approaches to scalar or tensorial Minkowski functionals in
mathematics and in physics, hence making the mathematical measure theoretic
method more readily accessible for future application in the physical sciences
Protein sequence and structure: Is one more fundamental than the other?
We argue that protein native state structures reside in a novel "phase" of
matter which confers on proteins their many amazing characteristics. This phase
arises from the common features of all globular proteins and is characterized
by a sequence-independent free energy landscape with relatively few low energy
minima with funnel-like character. The choice of a sequence that fits well into
one of these predetermined structures facilitates rapid and cooperative
folding. Our model calculations show that this novel phase facilitates the
formation of an efficient route for sequence design starting from random
peptides.Comment: 7 pages, 4 figures, to appear in J. Stat. Phy
Monolayers of hard rods on planar substrates. II. Growth
Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, “standing-up” transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion
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